# Mathematical Techniques for Managers | Browse Solutions

1) a. Solve the following system of linear equations by using elimination method.
− =
=
b. Let = [
1 2
5 3
],
= [
7
5
−3
1 2
] and = [
1 −3
− 1 2
] be two matrices.

Find the value of and if − = × , where , is the identity matrix and is the null
matrix.
2) Solve the following system of linear equations by using Cramer’s Rule. (20 Marks)
12 =
− =
10 =
3)
a. Solve the following system of linear equations by using inverse matrix method.
− =
=
b. Suppose that a company produced and sold two types of products. If they sold monthly 1 items
of one of the products at the rate of baisa per item and 2 items of second product at the rate
of baisa per item. Estimate the income if they sold 32000 items of first product and 55000 items
of second product in a year.
4) a. Suppose that a man has goat ( ) farm and there were 250 goats in the year and in the year ,
the number of goats increased to 450.

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i. Express the number of goats ( ) as a linear function of time
ii. Estimate the number of goats for the year 2025.
Note that is year in which your father borne (Father’s birth year) and is the year in which you
borne (Yours birth year).
b. A manufacturing factory sold items at the price RO per item. They described a profit
function ( ) = − . Find the number of items in order the company will be at breakeven
point.5)
Using EXCEL
Solve the following system of linear equations by using

a. Cramer’s Rule.
b. Inverse Matrix Method 1 =
− =
10 = �

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